On a Hele--Shaw-Type Domain Evolution with Convected Surface Energy Density

Matthias Günther, Georg Prokert
2005 SIAM Journal on Mathematical Analysis  
Interest is directed to a moving boundary problem with a gradient flow structure which generalizes surface-tension driven Hele-Shaw flow to the case of nonconstant surface tension coefficient taken along with the liquid particles at the boundary. In the case with kinetic undercooling regularization well-posedness of the resulting evolution problem in Sobolev scales is proved, including cases in which the surface tension coefficient degenerates. The problem is reformulated as a vector-valued,
more » ... enerate parabolic Cauchy problem. To solve this, we prove and apply an abstract result on Galerkin approximations with variable bilinear forms.
doi:10.1137/s0036141004444846 fatcat:p3he53jtfrcvnnncbiqkuy2es4